JOURNAL OF CHEMICAL PHYSICS
VOLUME 119, NUMBER 20
22 NOVEMBER 2003
Studies of metal hydrosulfides III: The millimeterÕsubmillimeter
spectrum of BaSH „ X̃ 2 A ⬘ …
A. Janczyk and L. M. Ziurys
Department of Astronomy, Department of Chemistry, Steward Observatory, University of Arizona,
Tucson, Arizona 85721
共Received 25 July 2003; accepted 2 September 2003兲
The pure rotational spectrum of BaSH (X̃ 2 A ⬘ ) and that of its deuterium isotopomer were measured
using millimeter direct absorption techniques in the range 305–365 GHz. This work is the first time
barium hydrosulfide has been observed by any spectroscopic technique. These radicals were
synthesized in a dc discharge by the reaction of barium vapor, produced in a Broida-type oven, and
either H2 S or D2 S. Thirteen rotational transitions of BaSH were recorded, as well as five transitions
of BaSD; for each transition, asymmetry components for K a ⫽0 through K a ⫽6 or 7 were typically
measured. Fine structure splittings, which generally ranged from 52 to 62 MHz in magnitude, were
also observed in every transition. These data unambiguously demonstrate that BaSH is a bent
molecule with C s symmetry, following the trend established in the lighter alkaline earth
hydrosulfides. Perturbations were found in the pure rotational spectra, however, likely resulting
from accidental degeneracies and strong vibration-rotation coupling. From these measurements,
rotational and fine structure parameters were established for BaSH and BaSD. An r 0 analysis
indicates that the Ba–S–H angle is 88°, while r Ba–S⫽2.807 Å and r S–H⫽1.360 Å. A comparison of
spin-rotation parameters with other hydrosulfides suggests that this interaction is dominated by
second-order spin–orbit contributions in BaSH, generated by rotational mixing of nearby excited
electronic states. Calculation of the g-tensor values for the unpaired electron in this radical suggests
an elongated distribution about the metal atom primarily along the ĉ axis, in contrast to MgSH and
CaSH, where the major asymmetry lies along the b̂ axis. © 2003 American Institute of Physics.
关DOI: 10.1063/1.1621381兴
I. INTRODUCTION
The differences between metal–oxygen bonds and their
sulfur analogs are of experimental and theoretical interest.1,2
Both types of bonds are found in a wide variety of chemical
environments, ranging from electrode materials to enzyme
centers.3,4 From a simplistic viewpoint, the electronegativity
in oxygen is larger than sulfur by a significant amount.
Therefore, it is perhaps to be expected that M–O bonds are
more ionic than their M–S counterparts. This trend is certainly observed in 3d transition metal diatomics, where examination of the metal hyperfine structure shows a decrease
in the Fermi contact term from MnO to MnS, and hence a
decrease in ionicity.5,6
Perhaps one of the most interesting systems for this
comparison is the MOH/MSH series. Metal monohydroxides
are fairly well studied spectroscopically. For example, the
alkali metal hydroxides were investigated in the 1960s and
1970s by Lide and co-workers7,8 and Kuijpers and
co-workers9,10 via pure rotational spectroscopy. Both optical
and rotational studies have been conducted for alkaline earth
hydroxides, MgOH to BaOH.11–15 Some of the IIIA group, as
well as a few transition metal hydroxides, have been investigated as well,16,17 including CuOH and AgOH.18 These
compounds overall have been found to exhibit a range of
geometries. Most of the metal hydroxides are linear—those
with Li, Ca, Sr, Ba, and Al, for example 共see Refs. 19, 11, 12,
13兲. A few have a bent geometry, namely copper and silver
0021-9606/2003/119(20)/10702/11/$20.00
hydroxide,18 and the F excited state of CaOH.20 Several such
species have been found to exhibit quasilinear behavior, including MgOH 共Ref. 21兲 and NaOH.10 Clearly, there is competition in these species between covalent and ionic bonding,
which favor bent and linear structures, respectively.21
In contrast, the MSH series is not as well characterized,
although it is slowly becoming so. Some of the alkali and
alkaline earth compounds have been investigated spectroscopically, including MgSH,22 CaSH,23,24 and NaSH,25 via
both electronic and millimeter methods. More recently, the
pure rotational spectrum of LiSH 共Ref. 26兲 and SrSH 共Ref.
27兲 have been recorded as well. In contrast to the hydroxides,
these metal hydrosulfides, as they are called, are all found to
be bent with an angle near 90°—even those that might be
considered very ionic, such as NaSH. The metal hydrosulfides therefore closely resemble H2 S in their structures and
consequently are predominately covalent compounds. This
characteristic apparently enables these simple triatomic species to be good model systems for the thiols RSH, where R is
an alkyl group.28
For several years, our group has been investigating metal
monohydroxide species using pure rotational spectroscopy
techniques, in particular the alkaline earth group 共e.g., Refs.
21, 29兲, LiOH,19 and AlOH.16 Very recently, we have begun
investigating some sulfur analogs as well, including SrSH,27
LiSH,26 and CuSH.30 Here we present our most recent work:
the measurement of the pure rotational spectrum of BaSH in
10702
© 2003 American Institute of Physics
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J. Chem. Phys., Vol. 119, No. 20, 22 November 2003
its X̃ 2 A ⬘ ground state. This study is the first time this radical
has been investigated by any spectroscopic method; it is also
the next species of interest in the alkaline earth series. Thirteen transitions of BaSH and five transitions of BaSD were
recorded, each consisting of multiple K a components which
are all split by spin-rotation interactions. Several perturbations were observed in the pure rotational data as well. In
this paper we present these results, their analysis, and a comparison with the geometric and electronic properties of other
alkaline earth hydrosulfides.
II. EXPERIMENT
The pure rotational spectra of BaSH and BaSD were
measured using one of the millimeter wave spectrometers of
the Ziurys group, which is described in detail elsewhere.31 To
point out the most important features, the source of radiation
consists of phase-locked Gunn oscillators combined with
Schottky diode multipliers. The reaction cell is a double-path
system with an attached Broida-type oven. The radiation is
focused through this chamber with a series of Teflon lenses
and a polarizing grid. The detector is a helium-cooled, InSb
hot electron bolometer.
BaSH was synthesized in a dc discharge from the reaction of barium vapor, created in a Broida-type oven, and
H2 S. BaSD was produced using D2 S 共Cambridge Laboratories兲. Approximately 1 mTorr of reactant gas was mixed with
about 5 mTorr of argon and introduced into the reaction
chamber over the top of the oven. Argon 共⬃10 mTorr兲 was
also flowed from beneath the oven as a carrier gas for the
metal vapor. The dc discharge was found to be essential to
create both radicals, and was typically run at 60 V and 0.21
A. Adjustment of the oven temperature was also critical. The
temperature had to be held at just above the melting point of
barium or the signals disappeared. The reaction mixture typically emitted a pale green color, indicative of the presence of
barium vapor. In addition to BaSH, BaS was synthesized in
large abundances. In fact, the signals due to BaS were by far
the strongest and often masked BaSH features.
In searching for the spectrum of BaSH, successive scans
covering 100 MHz in frequency were initially recorded. Actual frequency determinations were obtained from 5 MHz
scans, and by fitting Gaussian curves to the spectral features.
The 5 MHz data were always an average of an equal number
of scans in increasing and decreasing frequency. As many as
12 such averages were found necessary for weaker features.
III. RESULTS
The initial search for the rotational spectrum of BaSH
was based on the assumption that it had a bent geometry. The
Ba–S bond length was estimated to be 2.78 Å by scaling
from SrSH,27 using the SrS/BaS bond length ratio.32 The
S–H bond distance was taken to be 1.36 Å, based on the
other alkaline earth hydrosulfides.23,27 A bond angle of 90°
was assumed, as well. Based on these estimates, the effective
rotational constant for BaSH was found to be ⬃2.4 GHz.
Consequently, a total range of 23 GHz was searched, which
covered approximately 10 B eff . The search was conducted in
the 355–378 GHz range, where the Boltzmann distribution
The spectrum of BaSH
10703
reached a maximum at 100–200 °C. Because BaSH has one
unpaired electron, doublets were sought with a spin-rotation
splitting near 60–70 MHz, extrapolated from BaOH.33
A-type transitions are the strongest for this molecule, and
hence a spectrum was sought with transitions for which
⌬K a ⫽0.
Because BaS signals dominated the spectrum, lines
originating from all six barium isotopes of this molecule
were initially identified ( v ⫽0 – 6). Then, three sets of spinrotation doublets were located that were attributed to the
K a ⫽0, 4, 5, and 6 asymmetry components of BaSH, based
on their relative spacing. These features were found 6 GHz
from their predicted frequencies. Once these lines were assigned, the K a ⫽2 transitions, which were substantially split
by asymmetry doubling, were then identified. Finally, the
K a ⫽1 asymmetry doublets were found on the basis of their
predicted separation of 1.7 GHz. With these assignments in
place, the data could be fit with sufficient accuracy to predict
the position of the K a ⫽3 transitions. The lines were in general sufficiently weak such that only the main barium isotope
138
BaSH could be identified.
The initial search for BaSD was conducted over a continuous range of 324 –348 GHz, covering almost 11 B. The
assignment of the BaSD lines was more difficult because
their intensities were weaker and the spectra were contaminated by BaS and other unidentified features. The K a ⫽4, 5,
6, and 7 transitions were initially found, based on their relative splittings. However, as it turned out, the K a ⫽6 and 7
components were perturbed, making it difficult to establish
the pattern of the remaining K a components. A region 400
MHz to higher frequency of the K a ⫽4 lines was subsequently rescanned, with considerable signal-averaging, for
several transitions. The K a ⫽0, 2, and 3 components were
finally located based on the position of the K a ⫽5 line, and
then the K a ⫽1 lines were identified as well, using their predicted splitting of 2.7 GHz as a guideline.
Once the general patterns were established for BaSH and
BaSD, additional rotational transitions could be accurately
predicted. Hence, additional measurements required minimal
searching. No evidence of proton or deuterium hyperfine
splittings was observed in any of the data. Because only high
N transitions were recorded, the absence of hyperfine interactions is not surprising.
A subset of transitions measured for BaSH and BaSD are
presented in Table I. 共The complete data set is given in
EPAPS.34兲 Thirteen rotational transitions total were recorded
for BaSH in the range 305–365 GHz; for nine of them,
asymmetry components K a ⫽0 – 6 were measured. For the
remaining three transitions, which were the lower frequency
ones, only K a ⫽0 and 1 lines were obtained. Every transition
was split by ⬃52– 62 MHz due to spin-rotation interactions,
as indicated by quantum number J, and the K a ⫽1 and 2
components were additionally split because of asymmetry
doubling. In all other components, the asymmetry splitting
was too small to be observed, except for the K a ⫽3 lines,
which appeared broader than expected. A total of 191 individual lines were measured for BaSH.
In the case of BaSD, five rotational transitions were
measured, which are listed in Table I. In this case, K a com-
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10704
J. Chem. Phys., Vol. 119, No. 20, 22 November 2003
A. Janczyk and L. M. Ziurys
TABLE I. Observed rotational transitions of BaSH and BaSD (X̃ 2 A ⬘ ). a
BaSH
N⬘
K a⬘
K c⬘
J⬘ ← N⬙
64
64
64
64
64
64
65
65
65
65
65
66
66
66
66
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
67
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
1
1
0
0
1
1
1
1
0
0
1
1
1
0
1
1
1
6
6
5
5
5
5
4
4
4
4
3
3
3
3
2
2
2
0
2
1
1
1
1
7
7
7
7
6
6
6
6
5
5
5
5
4
4
4
4
3
3
3
3
2
0
2
0
2
64
64
64
64
63
63
65
65
65
65
64
66
66
66
65
67
67
62
61
63
62
63
62
64
63
64
63
65
64
65
64
66
66
65
67
65
66
66
70
70
64
63
64
63
65
64
65
64
66
65
66
65
67
66
67
66
68
67
68
67
69
70
69
70
68
63.5
64.5
63.5
64.5
63.5
64.5
64.5
65.5
64.5
65.5
64.5
65.5
66.5
66.5
65.5
66.5
67.5
66.5
66.5
66.5
66.5
67.5
67.5
66.5
66.5
67.5
67.5
66.5
66.5
67.5
67.5
66.5
67.5
66.5
67.5
67.5
66.5
67.5
69.5
70.5
69.5
69.5
70.5
70.5
69.5
69.5
70.5
70.5
69.5
69.5
70.5
70.5
69.5
69.5
70.5
70.5
69.5
69.5
70.5
70.5
69.5
69.5
70.5
70.5
69.5
63
63
63
63
63
63
64
64
64
64
64
65
65
65
65
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
66
69
69
69
69
69
69
69
69
69
69
69
69
69
69
69
69
69
69
69
69
69
69
69
69
69
69
69
BaSD
K a⬙
K c⬙
J⬙
␯ obs
␯ cal⫺ ␯ obs
1
1
0
0
1
1
1
1
0
0
1
1
1
0
1
1
1
6
6
5
5
5
5
4
4
4
4
3
3
3
3
2
2
2
0
2
1
1
1
1
7
7
7
7
6
6
6
6
5
5
5
5
4
4
4
4
3
3
3
3
2
0
2
0
2
63
63
63
63
62
62
64
64
64
64
63
65
65
65
64
66
66
61
60
62
61
62
61
63
62
63
62
64
63
64
63
65
65
64
66
64
65
65
69
69
63
62
63
62
64
63
64
63
65
64
65
64
66
65
66
65
67
66
67
66
68
69
68
69
67
62.5
63.5
62.5
63.5
62.5
63.5
63.5
64.5
63.5
64.5
63.5
64.5
65.5
65.5
64.5
65.5
66.5
65.5
65.5
65.5
65.5
66.5
66.5
65.5
65.5
66.5
66.5
65.5
65.5
66.5
66.5
65.5
66.5
65.5
66.5
66.5
65.5
66.5
68.5
69.5
68.5
68.5
69.5
69.5
68.5
68.5
69.5
69.5
68.5
68.5
69.5
69.5
68.5
68.5
69.5
69.5
68.5
68.5
69.5
69.5
68.5
68.5
69.5
69.5
68.5
305 678.225
305 740.139
306 367.699
306 426.628
307 110.389
307 165.851
310 422.979
310 484.906
311 118.494
311 180.554
311 876.753
315 166.170
315 228.226
315 932.809
316 641.683
319 908.025
319 969.964
320 022.056
320 022.056
320 226.867
320 226.867
320 281.717
320 281.717
320 395.943
320 395.943
320 451.230
320 451.230
320 530.666b
320 530.666b
320 586.243b
320 586.243b
320 606.707
320 662.975
320 670.046
320 683.546
320 724.879
321 404.999
321 459.866
334 123.864
334 186.021
0.017
⫺0.032
0.043
0.013
0.004
0.027
0.031
⫺0.029
0.004
0.064
⫺0.024
⫺0.033
0.012
0.004
0.030
0.077
⫺0.022
⫺0.032
⫺0.032
⫺0.020
⫺0.020
⫺0.013
⫺0.013
0.048
0.047
0.035
0.034
¯
¯
¯
¯
⫺0.001
⫺0.029
⫺0.012
0.010
⫺0.045
0.010
⫺0.001
⫺0.043
⫺0.004
334 244.293
334 244.293
334 298.733
334 298.733
334 458.167
334 458.167
334 512.985b
334 512.985b
334 634.778
334 634.778
334 690.170
334 690.170
334 775.764b
334 775.764b
334 831.389b
334 831.389b
334 853.423
334 867.448
334 909.783
⫺0.040
⫺0.040
0.046
0.046
0.010
0.010
0.016
0.015
⫺0.003
⫺0.004
¯
¯
¯
¯
0.001
⫺0.001
⫺0.021
␯ obs
␯ obs⫺ ␯ calc
324 300.148
324 867.790
324 867.790
324 921.407
324 921.407
325 107.555
325 107.555
325 161.359
325 161.359
325 313.551
325 313.551
325 367.570
325 367.570
325 488.960
325 488.960
325 543.057
325 543.057
325 636.986
325 650.553
325 690.997
325 704.261
325 604.011
325 296.357
325 659.629
325 356.233
326 048.263
⫺0.003
¯
¯
¯
¯
¯
¯
¯
¯
0.016
0.015
0.003
0.002
0.112
⫺0.042
0.088
⫺0.060
0.052
0.120
⫺0.048
⫺0.014
0.038
0.021
⫺0.018
⫺0.032
⫺0.033
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J. Chem. Phys., Vol. 119, No. 20, 22 November 2003
The spectrum of BaSH
10705
TABLE I. 共Continued.兲
BaSH
N⬘
K a⬘
K c⬘
70
70
70
71
71
71
71
71
71
71
71
71
71
71
71
71
71
71
71
71
71
71
71
71
71
71
71
71
71
71
71
71
71
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
73
73
73
73
73
2
1
1
1
1
7
7
7
7
6
6
6
6
5
5
5
5
4
4
4
4
3
3
3
3
2
0
2
0
2
2
1
1
1
7
7
6
6
6
6
5
5
5
5
4
4
4
4
3
3
3
3
2
0
2
0
2
2
1
1
1
1
7
7
7
68
69
69
71
71
65
64
65
64
66
65
66
65
67
66
67
66
68
67
68
67
69
68
69
68
70
71
70
71
69
69
70
70
72
66
65
67
66
67
66
68
67
68
67
69
68
69
68
70
69
70
69
71
72
71
72
70
70
71
71
73
73
67
66
67
J⬘ ← N⬙
70.5
69.5
70.5
70.5
71.5
70.5
70.5
71.5
71.5
70.5
70.5
71.5
71.5
70.5
70.5
71.5
71.5
70.5
70.5
71.5
71.5
70.5
70.5
71.5
71.5
70.5
70.5
71.5
71.5
70.5
71.5
70.5
71.5
72.5
71.5
71.5
71.5
71.5
72.5
72.5
71.5
71.5
72.5
72.5
71.5
71.5
72.5
72.5
71.5
71.5
72.5
72.5
71.5
71.5
72.5
72.5
71.5
72.5
71.5
72.5
72.5
73.5
72.5
72.5
73.5
69
69
69
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
70
71
71
71
71
71
71
71
71
71
71
71
71
71
71
71
71
71
71
71
71
71
71
71
71
71
71
71
72
72
72
72
72
BaSD
K a⬙
K c⬙
J⬙
␯ obs
␯ cal⫺ ␯ obs
␯ obs
␯ obs⫺ ␯ calc
2
1
1
1
1
7
7
7
7
6
6
6
6
5
5
5
5
4
4
4
4
3
3
3
3
2
0
2
0
2
2
1
1
1
7
7
6
6
6
6
5
5
5
5
4
4
4
4
3
3
3
3
2
0
2
0
2
2
1
1
1
1
7
7
7
67
68
68
70
70
64
63
64
63
65
64
65
64
66
65
66
65
67
66
67
66
68
67
68
67
69
70
69
70
68
68
69
69
71
65
64
66
65
66
65
67
66
67
66
68
67
68
67
69
68
69
68
70
71
70
71
69
69
70
70
72
72
66
65
66
69.5
68.5
69.5
69.5
70.5
69.5
69.5
70.5
70.5
69.5
69.5
70.5
70.5
69.5
69.5
70.5
70.5
69.5
69.5
70.5
70.5
69.5
69.5
70.5
70.5
69.5
69.5
70.5
70.5
69.5
70.5
69.5
70.5
71.5
70.5
70.5
70.5
70.5
71.5
71.5
70.5
70.5
71.5
71.5
70.5
70.5
71.5
71.5
70.5
70.5
71.5
71.5
70.5
70.5
71.5
71.5
70.5
71.5
70.5
71.5
71.5
72.5
71.5
71.5
72.5
334 980.281
335 685.499
335 737.089
338 859.374
338 921.536
⫺0.024
⫺0.028
⫺0.029
⫺0.016
⫺0.002
338 981.940
338 981.940
339 036.395
339 036.395
339 198.794
339 198.794
339 253.808
339 253.808
339 377.934
339 377.934
339 433.354
339 433.354
339 521.030b
339 521.030b
339 576.686b
339 576.686b
339 599.147
339 611.809
339 655.547
339 670.161
339 674.265
339 729.080
340 442.445
340 493.948
343 655.408
⫺0.013
⫺0.013
0.025
0.025
0.014
0.014
⫺0.020
⫺0.020
0.018
0.016
⫺0.009
⫺0.011
¯
¯
¯
¯
0.002
0.003
⫺0.010
0.020
⫺0.006
0.000
⫺0.027
⫺0.013
⫺0.020
343 717.918
343 717.918
343 772.455
343 772.455
343 937.848
343 937.848
343 992.793
343 992.793
344 119.472
344 119.472
344 174.906
344 174.906
344 264.591b
344 264.591b
344 320.391b
344 320.391b
344 343.233
344 354.324
344 399.668
344 412.613
344 421.524
344 476.305
345 197.754
345 249.216
348 325.462
348 387.654
⫺0.053
⫺0.053
0.005
0.005
0.050
0.050
⫺0.102
⫺0.102
0.007
0.005
⫺0.042
⫺0.044
¯
¯
¯
¯
⫺0.006
⫺0.005
⫺0.013
0.019
0.009
⫺0.004
⫺0.007
0.011
⫺0.006
⫺0.021
326 098.948
326 991.976
327 042.968
328 831.287
328 892.659
329 472.037
329 472.037
329 525.568
329 525.568
329 715.226
329 715.226
329 768.971
329 768.971
329 924.258
329 924.258
329 978.289
329 978.289
330 102.445
330 102.445
330 156.543
330 156.543
330 252.862
330 267.396
330 307.049
330 321.232
330 216.144
329 893.857
330 271.795
329 953.894
330 678.863
330 729.406
331 621.590
331 672.629
333 483.507
334 074.560
334 074.560
334 321.270
334 321.270
334 375.130
334 375.130
334 533.403
334 533.403
334 587.461
334 587.461
334 714.412
334 714.412
334 768.514
334 768.514
334 867.400
⫺0.016
0.026
0.003
0.036
⫺0.015
¯
¯
¯
¯
¯
¯
¯
¯
⫺0.004
⫺0.005
⫺0.016
⫺0.017
0.077
⫺0.092
0.054
⫺0.111
⫺0.073
⫺0.017
0.008
⫺0.002
0.010
0.019
⫺0.043
⫺0.002
0.011
⫺0.027
0.019
⫺0.013
⫺0.006
¯
¯
¯
¯
¯
¯
⫺0.012
⫺0.013
⫺0.007
⫺0.008
0.087
⫺0.100
0.067
⫺0.114
0.022
334 921.505
334 936.645
334 826.612
334 489.258
0.026
⫺0.043
0.003
⫺0.022
334 549.468
335 308.143
335 358.669
336 249.403
336 300.352b
338 011.170
338 072.668
338 675.558
338 675.558
338 729.236
0.000
⫺0.024
0.006
0.010
0.013
0.023
¯
¯
¯
Downloaded 16 Aug 2004 to 129.132.73.140. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp
10706
J. Chem. Phys., Vol. 119, No. 20, 22 November 2003
A. Janczyk and L. M. Ziurys
TABLE I. 共Continued.兲
BaSH
N⬘
K a⬘
K c⬘
73
73
73
73
73
73
73
73
73
73
73
73
73
73
73
73
73
73
73
73
73
73
73
73
73
74
74
74
74
74
74
74
74
74
74
74
74
74
74
74
74
74
74
74
74
74
74
74
74
74
74
74
74
74
74
7
6
6
6
6
5
5
5
5
4
4
4
4
3
3
3
3
2
0
2
0
2
2
1
1
1
1
7
7
7
7
6
6
6
6
5
5
5
5
4
4
4
4
3
3
3
3
2
0
2
0
2
2
1
1
66
68
67
67
68
69
68
69
68
70
69
70
69
71
70
71
70
72
73
72
73
71
71
72
72
74
74
68
67
68
67
69
68
69
68
70
69
70
69
71
70
71
70
72
71
72
71
73
74
73
74
72
72
73
73
J⬘ ← N⬙
73.5
72.5
72.5
73.5
73.5
72.5
72.5
73.5
73.5
72.5
72.5
73.5
73.5
72.5
72.5
73.5
73.5
72.5
72.5
73.5
73.5
72.5
73.5
72.5
73.5
73.5
74.5
73.5
73.5
74.5
74.5
73.5
73.5
74.5
74.5
73.5
73.5
74.5
74.5
73.5
73.5
74.5
74.5
73.5
73.5
74.5
74.5
73.5
73.5
74.5
74.5
73.5
74.5
73.5
74.5
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
72
73
73
73
73
73
73
73
73
73
73
73
73
73
73
73
73
73
73
73
73
73
73
73
73
73
73
73
73
73
73
K a⬙
K c⬙
J⬙
7
6
6
6
6
5
5
5
5
4
4
4
4
3
3
3
3
2
0
2
0
2
2
1
1
1
1
7
7
7
7
6
6
6
6
5
5
5
5
4
4
4
4
3
3
3
3
2
0
2
0
2
2
1
1
65
67
66
66
67
68
67
68
67
69
68
69
68
70
69
70
69
71
72
71
72
70
70
71
71
73
73
67
66
67
66
68
67
68
67
69
68
69
68
70
69
70
69
71
70
71
70
72
73
72
73
71
71
72
72
72.5
71.5
71.5
72.5
72.5
71.5
71.5
72.5
72.5
71.5
71.5
72.5
72.5
71.5
71.5
72.5
72.5
71.5
71.5
72.5
72.5
71.5
72.5
71.5
72.5
72.5
73.5
72.5
72.5
73.5
73.5
72.5
72.5
73.5
73.5
72.5
72.5
73.5
73.5
72.5
72.5
73.5
73.5
72.5
72.5
73.5
73.5
72.5
72.5
73.5
73.5
72.5
73.5
72.5
73.5
BaSD
␯ obs
␯ cal⫺ ␯ obs
348 452.397
348 452.397
348 506.925
348 506.925
348 675.382b
348 675.382b
348 730.327
348 730.327
348 859.387
348 859.387
348 914.874
348 914.874
349 006.639b
349 006.639b
349 062.350b
349 062.350b
349 085.690
349 095.075
349 142.158
349 153.361
349 167.212
349 221.985
349 951.356
350 002.801
353 055.972
353 118.244
0.032
0.032
0.022
0.022
¯
¯
⫺0.007
⫺0.007
0.001
⫺0.001
⫺0.031
⫺0.033
¯
¯
¯
¯
0.009
0.008
0.004
0.041
0.022
0.014
⫺0.015
0.002
⫺0.044
⫺0.010
353 185.079
353 185.079
353 239.710
353 239.710
353 410.977
353 410.977
353 466.107
353 466.107
353 597.718
353 597.718
353 653.165
353 653.165
353 747.011b
353 747.011b
353 802.746b
353 802.746b
353 826.410
353 834.028
353 882.968
353 892.326
353 911.290
353 966.055
354 703.233
354 754.707
⫺0.032
⫺0.032
0.001
0.001
0.048
0.048
⫺0.016
⫺0.016
0.061
0.059
⫺0.047
⫺0.049
¯
¯
¯
¯
⫺0.039
0.002
0.015
0.031
0.014
0.013
⫺0.045
0.001
␯ obs
␯ obs⫺ ␯ calc
338 729.236
338 925.713
338 925.713
338 979.625
338 979.625
339 140.981
339 140.981
339 195.033
339 195.033
339 324.776
339 324.776
339 378.934
339 378.934
339 480.213
339 496.823
339 534.363
339 550.602
339 435.373
339 082.607
339 491.123
339 142.942
¯
¯
¯
¯
¯
0.009
0.008
0.000
⫺0.002
0.079
⫺0.126
0.116
⫺0.084
⫺0.026
⫺0.018
0.028
⫺0.016
0.000
⫺0.031
⫺0.012
⫺0.013
339 986.648
340 875.366
340 926.609
342 598.502
342 660.081
343 274.927
343 274.927
343 328.612
343 328.612
343 528.605
343 528.605
343 582.507
343 582.507
343 746.888
343 746.888
343 801.017
343 801.017
343 933.568
343 933.568
343 987.721
343 987.721
344 091.498
344 109.226
344 145.604
344 163.044
344 042.381
343 673.858
344 098.195
343 734.373
344 562.991
344 613.330
345 499.514
345 550.829
0.015
⫺0.024
0.024
⫺0.025
0.035
¯
¯
¯
¯
¯
¯
¯
¯
⫺0.021
⫺0.023
0.037
0.036
0.106
⫺0.119
0.139
⫺0.080
0.001
⫺0.023
0.018
0.041
⫺0.022
⫺0.030
0.000
0.037
0.010
0.007
⫺0.019
0.031
In MHz, for v ⫽0.
Blended lines.
a
b
ponents 0–7 were recorded for every transition, a total of
105 individual features. Here the asymmetry doubling was
resolved in the K a ⫽1, 2, and 3 components. The typical
spin-rotation splitting in barium deuterosulfide was 51– 61
MHz.
In Fig. 1, representative spectra for BaSH and BaSD are
presented, which are sufficient evidence for C s symmetry in
both species. In the upper panel, a section of the N⫽75
→76 transition of BaSH is shown near 363 GHz. The K a
components present in this part of the spectrum are split into
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J. Chem. Phys., Vol. 119, No. 20, 22 November 2003
FIG. 1. Spectra showing portions of the N⫽75→76 rotational transition of
BaSH near 363 GHz 共top panel兲 and the N⫽72→73 transition of BaSD near
339 GHz 共bottom panel兲, both in their X̃ 2 A ⬘ ground electronic states. Quantum number labeling is N(K a ,K c ). Unidentified features are marked by
asterisks, and a line of BaS( v ⫽6) appears in the BaSD data. Spin-rotation
splittings are clearly visible in each transition, indicated by brackets. The
BaSH spectrum displays the K a ⫽0, 3, and 4 asymmetry components, as
well as one asymmetry doublet for K a ⫽2. The BaSD spectrum shows the
K a ⫽0, 4, and 5 asymmetry components; the K a ⫽4 and 5 transitions are
shifted to higher frequency relative to the K a ⫽0 lines in BaSD, unlike
BaSH. Each spectrum is a composite of three, 100 MHz scans, each recorded in ⬃1 min.
doublets, separated by about 60 MHz, which arise from spinrotation interactions. The asymmetry doubling is collapsed in
the K a ⫽3 and 4 components, and only one of the K a ⫽2
asymmetry pairs appears in this frequency range, almost coincident with the K a ⫽0 doublet. Features marked by asterisks are unidentified lines.
In the lower panel, a section of the N⫽72→73 transition
of BaSD near 339 GHz is displayed. Again, the spin-rotation
doublets are visible in each spectrum, and no asymmetry
splittings are resolved in the K a ⫽4 and 5 features. The spectrum of the deuterated species shows significant change in
pattern relative to that of BaSH, as expected because the
asymmetry has increased. The K a ⫽4 and 5 components, for
example, lie higher in frequency relative to the K a ⫽0 features. A line of BaS originating in the v ⫽6 level also appears in the spectrum, and one unidentified feature.
Although most of the recorded transitions followed a
The spectrum of BaSH
10707
FIG. 2. Stick spectra displaying the positions and relative intensities of the
K a components of the N⫽66→67 transition of BaSH 共top panel兲 and the
N⫽70→71 transition of BaSD 共lower panel兲. Perturbations are illustrated in
each figure. For BaSH, one line of the spin-rotation doublet for the K a ⫽0
asymmetry component is not found at its expected frequency, and is clearly
shifted significantly in the pattern. ‘‘Missing’’ spin-rotation components
were found in several transitions. For BaSD, the K a ⫽6 and 7 asymmetry
components were found to be shifted to a lower frequency, relative to predictions based on the K a ⫽0 – 5 measurements.
regular, a-type, asymmetric top pattern, perturbations were
found in the spectrum of both BaSH and BaSD. These effects
are illustrated in Fig. 2, which show stick figures of the K a
progression in one transition of each of the two isotopomers.
For BaSH 共top figure兲, the K a ⫽0, J⫽65.5→66.5 spin component of the N⫽66→67 transition was found to be missing,
although the other pair of the doublet (J⫽66.5→67.5) was
clearly visible in the spectrum. The subsequent K a ⫽2, 3, 4,
and 5 components, in contrast, are all at the expected frequencies, as illustrated in the stick progression. Rescanning
and signal-averaging around the expected frequency of the
‘‘missing’’ line proved fruitless. In the adjacent N⫽65→66
transition, the K a ⫽0 (J⫽64.5→65.5) and K a ⫽1 (J⫽65.5
→66.5, K c ⫽N⫺1) lines were missing as well, although
their spin-rotation partners were readily visible in the data.
An identical situation was found for the K a ⫽1 component
for J⫽64.5→65.5, K c ⫽N⫺1. Once again, extensive signalaveraging failed to reveal any spectral lines at these frequencies. As will be discussed later, these lines are not really
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10708
J. Chem. Phys., Vol. 119, No. 20, 22 November 2003
TABLE II. Rotational constants for BaSH and BaSD (X̃ 2 A ⬘ ). a
A
B
C
DN
D NK
d1
d2
H NK
H KN
h3
L NK
L KKN
P KN
P NKK
⑀ aa
⑀ bb
⑀ cc
( ⑀ ab ⫹ ⑀ ba )/2
D NS
⌬ 0 (amu Å2 )
rms of fit
a
BaSH
BaSD
290 342共49兲
2413.2528共36兲
2390.6535共33兲
9.4901(15)⫻10⫺4
0.14232共82兲
⫺9.20(16)⫻10⫺6
⫺1.119(18)⫻10⫺6
1.31(79)⫻10⫺7
⫺1.08(62)⫻10⫺4
¯
1.08(58)⫻10⫺8
9.3(1.3)⫻10⫺6
⫺1.52(11)⫻10⫺7
⫺3.3(1.1)⫻10⫺10
308.7共9.9兲
45.09共18兲
66.98共15兲
⫺7.806共83兲
2.4(1.0)⫻10⫺9
0.239 04共52兲
0.032
149 030共48兲
2356.247共13兲
2316.145共12兲
9.4043(39)⫻10⫺4
0.13176共37兲
⫺1.670(55)⫻10⫺5
⫺3.253(31)⫻10⫺6
1.17(35)⫻10⫺7
1.34(24)⫻10⫺5
4.7(3.0)⫻10⫺12
176共20兲
44.17共17兲
65.56共12兲
⫺10.6共4.5兲
¯
0.3225共16兲
0.027
In MHz; errors are 3 sigma and apply to the last quoted decimal places.
missing but are significantly shifted in frequency by perturbations resulting from accidental degeneracies.
In BaSD 共see lower stick display in Fig. 2兲, the K a ⫽6
and K a ⫽7 asymmetry components were found to be perturbed. As the figure illustrates, these two components were
shifted to a lower frequency relative to their predicted values
by a significant amount 共⬃30 MHz兲. This effect was observed in every transition studied, and thus the K a ⫽6 and 7
lines could not be included in the final analysis.
IV. ANALYSIS
The data for BaSH and BaSD were analyzed using the
S-reduced Hamiltonian of Watson.35 This Hamiltonian consists of terms for molecular frame rotation, its centrifugal
distortion and the spin rotation. The Hamiltonian was incorporated into the nonlinear least squares code, SPFIT, of
Pickett.36
Only the K a ⫽0, 4, 5 were fit initially for BaSH. The
rotational constants A, B, and C, distortion constants D N and
D NK , and the spin rotational parameters ⑀ bb and ⑀ cc were
used in the first iteration. Because the asymmetry splitting is
absent in these components, B was set equal to C and ⑀ bb
⫽ ⑀ cc . As more K a components were added to the data set,
the number of constants was increased and B and C and ⑀ bb
and ⑀ cc were fit independently. A total of 18 parameters with
distortion terms up to 10th order were included in the final
analysis of BaSH, achieving a rms of 32 kHz, as shown in
Table II. 共The unresolved K a ⫽3 asymmetry doublets were
not included in the fit.兲
The BaSD was fit in a similar manner. A total of fourteen
constants were required for this isotopomer with distortion
terms up to sixth order. The perturbed K a ⫽6 and K a ⫽7
components were not included in the final analysis, where a
A. Janczyk and L. M. Ziurys
TABLE III. r 0 structures for alkali and alkaline earth hydrosulfides.
LiSH
NaSHa
MgSH
CaSH
SrSH
BaSH
a
r M–S 共Å)
r S–H 共Å)
␪ M–S–H 共deg)
2.146共1兲
2.479共1兲
2.316共15兲
2.564共6兲
2.706共3兲
2.807共3兲
1.353共1兲
1.354共1兲
1.339b
1.357共5兲
1.358共4兲
1.360共4兲
93.0共1兲
93.10共1兲
87共20兲
91共5兲
91.04共3兲
88.34共3兲
Structure refit from data in Ref. 25.
Held fixed.
b
rms value of 27 kHz was achieved. Fewer parameters were
needed to fit BaSD because a smaller range of transitions
was recorded.
Although many higher order parameters were used in the
analysis of BaSH, an almost identical set was employed to fit
the pure rotational spectrum of SrSH.27 This set includes the
tenth order centrifugal distortion term P KN . Sextic parameters were needed for the analysis of both CaSH 共Ref. 23兲
and MgSH,22 and an octic term for CaSD,23 as well. One
centrifugal distortion correction to the spin-rotation, D Ns ,
was also needed to fit SrSH,27 as well as for BaSH. For both
BaSH and BaSD, all constants are well-determined relative
to their 3␴ errors 共see Table II兲.
The zero-point inertial defects were additionally calculated for BaSH and BaSD, and are given in Table II. They
are 0.23904 amu Å2 and 0.3225 amu Å2, respectively. These
values are very similar to those determined for SrSH 共0.2303
amu Å2兲 and SrSD 共0.3146 amu Å2兲. From the combined
BaSH/BaSD data set, an r 0 structure was calculated for
barium hydrosulfide as well, using a nonlinear least-squares
fit to the moments of inertia. The resulting structure is presented in Table III.
V. DISCUSSION
A. Geometric differences in metal hydrosulfides
BaSH has not been studied previously by any spectroscopic technique. This study has demonstrated, however, that
this radical is clearly bent like its other alkaline earth and
alkali counterparts. In fact, it may be even more bent than the
other species, as shown in Table III.
Table III summarizes all available structural information
for metal hydrosulfides. As this table illustrates, the metal–
sulfur bond length correlates closely to the metal atomic radii. Hence, the largest metal–sulfur bond length is for BaSH,
the smallest for LiSH. In contrast, the sulfur–hydrogen bond
distances cluster around 1.356 Å. 共The S–H bond length in
MgSH was held fixed.兲 The most interesting geometric differences among these molecules concern the M–S–H bond
angles. Although the angles are all very close to that in
H2 S (92.1°), the alkali hydrosulfides NaSH and LiSH have
␪⯝93°. The alkaline earth species, on the other hand, have
angles ␪ⱗ91°. In fact, the value for BaSH is the smallest at
88.3°.
The one major difference between these hydrosulfides is
the presence of an unpaired electron on the alkaline earth
species; the alkali analogs, in contrast, are closed-shell. It
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J. Chem. Phys., Vol. 119, No. 20, 22 November 2003
The spectrum of BaSH
10709
FIG. 3. An energy level diagram displaying the N⫽64, 65, 66, and 67 levels for the K a ⫽0 and K a ⫽1, K c ⫽N,
and K c ⫽N⫺1 asymmetry components. Spin-rotation levels are indicated by quantum number J and have
⫹ or ⫺ parity. As shown in the figure,
some levels lie very close in energy
and hence perturb each other according to the selection rules, ⌬N⫽⫾1,
⌬J⫽0, ⫹↔⫹, ⫺↔⫺. This perturbation explains the large frequency shifts
of certain spin-rotation components in
the N⫽64→65, 65→66, and 66→67
transitions.
could be that this electron undergoes a certain degree of repulsion from the lone pair on the sulfur atom, hence slightly
closing the M–S–H angle for the alkaline earth series. Because BaSH has the largest metal atom with the unpaired
electron in the spatially extended 7s orbital, the repulsion is
perhaps largest in this particular species, and therefore the
M–S–H angle the smallest.
The bond angles in the hydrosulfides also suggest a lack
of hybridization of the orbitals on sulfur. Unlike H2 O, whose
bond angle of 105° is close to the tetrahedral angle, the
M–SH molecules have angles all near 90°. This property
suggests that the bonding of sulfur to the metal and the hydrogen atoms is primarily made through pure p-type orbitals.
B. Perturbations in the ground state
As mentioned, several perturbations were found in the
pure rotational spectrum of both BaSH and BaSD. In BaSH,
FIG. 4. A plot showing the normalized spin rotation constants ⑀ aa /A, ⑀ bb /B, and ⑀ cc /C for the alkaline earth hydrosulfides. If second-order spin–orbit effects
were not contributing to these constants, they should all have similar values. Instead, a large increase is seen in these normalized parameters, especially from
CaSH to BaSH. The effects are particularly pronounced for ⑀ bb /B and ⑀ cc /C, although a change also exists for ⑀ aa /A. These trends suggest that the
second-order contribution increases for the spin-rotation constant as the Periodic Table is descended.
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10710
J. Chem. Phys., Vol. 119, No. 20, 22 November 2003
the perturbations manifested themselves in the ‘‘disappearance’’ of one of the pairs of spin rotation doublets in the
several transitions. Specifically, the K a ⫽0, J⫽65.5→66.5
component of the N⫽66→67 transition could not be found,
as well as the K a ⫽1 (J⫽65.5→66.5, K c ⫽N⫺1) and K a
⫽0 (J⫽64.5→65.5) lines in the N⫽65→66 transition, and
the K a ⫽1 (J⫽64.5→65.5, K c ⫽N⫺1) feature for N⫽64
→65.
These transitions all originate or end at one of two energy levels: the N⫽66, J⫽65.5(⫹), K a ⫽0 and the N
⫽65, J⫽65.5(⫹), K a ⫽1, K c ⫽N⫺1 levels. A calculation
of the rotational energy levels of BaSH, based on the derived
constants, shows that these two levels lie at virtually the
same energy, 348 –353 cm⫺1, as shown in Fig. 3. They lie
close enough to perturb each other, following the selection
rules ⌬J⫽0, ⌬N⫽⫾1, and ⫹↔⫹. Hence, transitions involving these levels are shifted in the otherwise regular spectral progression. 共Possible candidates for the perturbed lines
have been identified in the spectra.兲
Further evidence for the interaction of nearby rotational
levels is found in the nonzero value determined for the offdiagonal spin-rotation term, ( ⑀ ab ⫹ ⑀ ba )/2, for both species.
This parameter arises from the operator N a S b ⫹N b S a , which
couples the fine structure levels J⫽N⫺ 21 , K a ⫽0 with J
⫽N⫹ 21 , K a ⫽1, K c ⫽N⫺1, if they have the same J quantum
number. Hence, this constant is needed in the data fit if such
coupling occurs. For BaSH, excluding ( ⑀ ab ⫹ ⑀ ba )/2 from the
analysis resulted in significantly larger residuals for many of
the K a ⫽0 and K a ⫽1 lines. The residuals increased in value
from an average 10 kHz, to as large as 4 MHz. A similar, but
less dramatic effect was noticed in the analysis of SrSH.27 In
this case, however, the expected level crossing occurred at J
values that were not studied; in this particular work ‘‘missing’’ features were not observed.
The major perturbation in BaSD occurred for the K a
⫽6 and K a ⫽7 components, which were shifted on the order
of 30 MHz from their predicted frequencies, based on the fit
obtained from the K a ⫽0 – 5 transitions. This shift occurred
in every transition. This perturbation is attributed to rotationvibration coupling. As the molecule rotates faster about the
â-axis, it becomes more bent, and therefore couples more
effectively to at least one bending mode.37 This effect in fact
can be tested by calculating the K a -dependent rotational constants via the following expressions:35
A. Janczyk and L. M. Ziurys
A eff⫽A⫺D K K 2a ,
共1兲
B eff⫽ 共 B⫹C 兲 /2⫺D NK K 2a ⫹H NK K 4a .
共2兲
The constant D K cannot be determined from the rotational
data recorded here. Hence, it was scaled from the value
found for CaSD by the ratio of rotational constants, resulting
in D K (BaSD)⫽46.7 MHz. Using these values and those of
the other parameters from the data fit, it was found that A eff
and B eff decreased by 0.2% and 0.4%, respectively, from
K a ⫽0 to K a ⫽5. Hence, the BaSD does become more bent
with increasing K a quantum number. This effect was not
noticeable in BaSH, where the K a ⫽6 components fit quite
reasonably. The rotation-vibration coupling is stronger in
BaSD because the vibrational modes likely lie lower in energy than in BaSH.
C. Spin-rotation interactions in the alkaline
earth series
The spin-rotation interaction consists generally of first
order and second order contributions. The first term is a measure of the coupling of the unpaired electrons to the rotating
molecular frame. It is proportional to the rotational
constant.38 The second order effect arises from indirect spin–
orbit coupling originating in nearby excited states. Therefore,
if the second order contribution is negligible, the spinrotation constants should scale as the B values.
The second order contribution is non-negligible for the
alkaline earth hydrosulfides, as illustrated in Fig. 4. This figure is a plot of the three spin rotation constants ⑀ aa , ⑀ bb , and
⑀ cc , normalized by their respective rotational constant A, B,
and C, for MgSH through BaSH. If the first order effects
dominated these constants, they should all be about the same
value on this graph. Instead, there is a significant increase in
both ⑀ bb /B and ⑀ cc /C from magnesium, to calcium, strontium, and finally to barium hydrosulfide. There is an increase
in ⑀ aa /A as well, although it is smaller relative to the others.
This graph suggests that the second order effects increase in
importance from magnesium to barium, as well.
This increase is expected on examining the origin of this
interaction. The second order spin-rotation interaction for
⑀ aa , ⑀ bb , and ⑀ cc in the ground state can be expressed as38
⑀ 共aa2 兲 ⫽⫺2
兺
␣ ⫽␣
具 ␣ 兩 aL z 兩 ␣ ⬘ 典具 ␣ ⬘ 兩 AL z 兩 ␣ 典 ⫹ 具 ␣ 兩 AL z 兩 ␣ ⬘ 典具 ␣ ⬘ 兩 aL z 兩 ␣ 典
⑀ 共bb2 兲 ⫽⫺2
兺
␣ ⫽␣
具 ␣ 兩 aL y 兩 ␣ ⬘ 典具 ␣ ⬘ 兩 BL y 兩 ␣ 典 ⫹ 具 ␣ 兩 BL y 兩 ␣ ⬘ 典具 ␣ ⬘ 兩 aL y 兩 ␣ 典
⑀ 共cc2 兲 ⫽⫺2
兺
␣ ⫽␣
具 ␣ 兩 aL x 兩 ␣ ⬘ 典具 ␣ ⬘ 兩 CL x 兩 ␣ 典 ⫹ 具 ␣ 兩 CL x 兩 ␣ ⬘ 典具 ␣ ⬘ 兩 aL x 兩 ␣ 典
⬘
⬘
⬘
E ␣ ⫺E ␣ ⬘
E ␣ ⫺E ␣ ⬘
E ␣ ⫺E ␣ ⬘
共3兲
,
,
共4兲
.
共5兲
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J. Chem. Phys., Vol. 119, No. 20, 22 November 2003
The spectrum of BaSH
Here, ␣ denotes the ground state and ␣⬘ indicates the perturbing excited states. L z , L x , and L y are the expectation
values of the orbital angular momentum, while A, B, and C
are rotational constants and a is the spin–orbit coupling
parameter.
In analogy to CaSH and SrSH,24 the nearby A, B, and
C excited states in BaSH likely have A ⬘ , A ⬙ , and A ⬘ symmetry. Hence, they will connect to the ground state (A ⬘
symmetry兲 via the orbital angular momentum operators
and the numerators will be nonzero, as for all the alkaline
earth hydrosulfides. The factors that will change the second
order contribution to the spin-rotation parameters for the
alkaline earth species are the excited-ground state energy
differences in the denominator, and the values of the spin–
orbit constant in the numerator. The energy differences
steadily decrease as the molecular mass increases. The
smallest difference will be for BaSH. Furthermore, the spin
orbit constants, based on atomic parameters of the alkaline earth metals, should increase down the periodic row.
共The atomic values are 40.5 cm⫺1, 87 cm⫺1, 387 cm⫺1, and
832 cm⫺1 for Mg, Ca, Sr, and Ba, respectively.39 The atomic
ion values follow a similar trend.兲 Overall, the second-order
contribution to the spin-rotation constants should significantly increase down the alkaline earth column, as has been
found.
On the other hand, the metal hydrosulfides have C s
symmetry and thus any electronic state can only have A ⬘ or
A ⬙ terms. These terms are not degenerate and have no orbital angular momentum. As described in Whitham and
Jungen,40 however, orbital angular momentum can be generated by rotation, which causes a ‘‘slipping’’ of the electron
orbit with respect to the molecular plane. The result of this
slippage is that p ⌸ character of the unpaired electron in the
nearby excited states mixes with the s electron of the ground
state.
The largest component of the spin-rotation tensor in the
case of BaSH is ⑀ aa , which has a value of 309 MHz, as
opposed to 45 MHz and 67 MHz, for ⑀ bb and ⑀ cc . A similar
trend is observed in BaSD 共see Table II兲. The ⑀ aa constant
has the greatest value because the largest rotational constant,
A, contributes to the second order effect, while B and C come
into play for the other two parameters. The ⑀ aa parameter is
in fact greater in BaSH than in SrSH, CaSH, or MgSH,
which have ⑀ aa ⫽52.6 MHz, ⫺14.4 MHz, and ⫺51.2 MHz,
respectively. The change in sign and magnitude occurs in a
uniform way, and may reflect the competition between first
and second order spin-rotation contributions, as noted by Liu
et al.38
The g-tensors for all four alkaline earth species have
been calculated using Curl’s formula,41
g ␣␣ ⬇g e ⫺
⑀ ␣␣
.
2B ␣
共6兲
These numbers are listed in Table IV. 共The deuterated species have virtually identical values, so they are not given.兲 As
illustrated in the table, the values for g aa are closest to the
free electron value of 2.00232 for all species. The most deviation from g e is seen for g cc in BaSH and g bb in CaSH and
MgSH, while for SrSH, g cc ⬇g bb . The unpaired electron on
10711
TABLE IV. g-tensors for alkaline earth hydrosulfides.
Molecule
a
MgSH
CaSHb
SrSHc
BaSH
g aa
g bb
g cc
2.002 41
2.002 34
2.002 23
2.001 79
1.997 61
1.996 96
1.992 56
1.992 98
1.998 80
1.997 75
1.992 00
1.988 31
a
Reference 22.
Reference 23.
c
Reference 27.
b
the metal atom in the ground state therefore does not have a
strictly spherical distribution; this result suggests that p ⌸
character is contributed from excited states, as mentioned.
However, the axis of highest asymmetry is dependent on the
metal atom.
This effect can perhaps be explained in terms of metal
atom size. Assuming no orbital hybridization, the lone electron pair on the sulfur atom in the hydrosulfides would be
located in a p orbital along the ĉ axis. Because the unpaired
electron in BaSH lies in essentially a large 7s atomic orbital,
it may undergo non-negligible repulsion by the sulfur lone
pair. Therefore, the distribution of the single metal electron
should be most elongated along the ĉ axis in BaSH, as reflected in g cc . In magnesium and calcium, the analogous
orbitals are not as large, and the unpaired electron is not
affected by the sulfur electrons. The axis of greatest asymmetry for these two molecules, as indicated by g bb , is the b̂
axis; this anisotropy may be generated by repulsion of the
electrons of the S–H bond. The two competing effects are
almost equal at SrSH, such that g bb ⬇g cc .
VI. CONCLUSION
The pure rotational spectrum of BaSH has been measured, proving that this molecule has a bent geometry and C s
symmetry, in analogy to the other alkaline earth hydrosulfides. The barium species appears to be slightly more bent
than the SrSH and CaSH, with a bond angle near 88°. Perturbations resulting from accidental degeneracies of the spinrotation levels were observed, shifting certain transitions
from the expected pattern. Higher K a components in BaSD
were also perturbed, a likely outcome of increased rotationvibration coupling. The spin-rotation constants in the barium
species were found to contain large second order contributions, on comparison with the other alkaline earth hydrosulfides. The relative values and signs of the diagonal terms of
the spin-rotation tensor also uniformly change from MgSH
through to BaSH, as reflected in the g-values. While BaSH
appears to be very similar to the other alkaline earth species,
a small but non-negligible redistribution of the unpaired
electron on the metal atom occurs for this species relative to
the lighter alkaline earth hydrosulfides.
ACKNOWLEDGMENT
This research is supported by NSF Grant No. CHE-9817707.
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10712
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